Conditional Variability of Statistical Shape Models Based on Surrogate Variables

Abstract

Abstract. We propose to increment a statistical shape model with surrogate variables such as anatomical measurements and patient-related information, allowing conditioning the shape distribution to follow prescribed anatomical constraints. The method is applied to a shape model of the human femur, modeling the joint density of shape and anatomical parameters as a kernel density. Results show that it allows for a fast, intuitive and anatomically meaningful control on the shape deformations and an effective conditioning of the shape distribution, allowing the analysis of the remaining shape variability and relations between shape and anatomy. The approach can be further employed for initializing elastic registration methods such as Active Shape Models, improving their regularization term and reducing the search space for the optimization.

Statistical model based shape prediction from a combination of direct observations and various surrogates: Application to orthopaedic research

“…In particular, the conditional expectation E½yjx can be considered as an estimate of the shape that best corresponds to the observed predictors. Two different models for the joint distribution Pðx; yÞ are considered here: a simple multivariate Gaussian model, and the kernel density model proposed in (Blanc et al, 2009). …”

“…It relies on the choice of a kernel function K H , where H is the kernel bandwidth. We choose a Gaussian kernel, and optimize its bandwidth through cross-validation as proposed in (Blanc et al, 2009).…”

“…Whenever gender was used as a predictor, the training matrices X and Y were replaced by the corresponding subset of training samples sharing the same gender. Kernel regression was performed as described in (Blanc et al, 2009), using the conditional expectation as the predicted shape. Finally, we compared the results with those obtained by calculating the conditional distribution assuming a joint Gaussian distribution between the predictors and the shape.…”

“…For a similar purpose, Ericsson et al (2008) proposed to use non-parametric regression. In (Blanc et al, 2009) a non-parametric approach for conditional shape modeling was introduced, which enables to constrain a statistical model simultaneously by several anthropometric and morphometric information. The results highlight the more compact model that can be attained by conditioning the space of plausible shapes, making the proposed method suitable to create patientspecific shape models, while reducing the space of the modeled shape variability.…”

Complete Valvular Heart Apparatus Model from 4D Cardiac CT

“…We use the fixed point algorithm to perform the Independent Component Analysis [13]. [14]. Assuming the joint multivariate distribution (V q | M) follows a Gaussian distribution a conditioned surface V M q , containing the anatomical measurements M, can be estimated as follows:…”